Necessary and Sufficient Conditions for the Existence of a Classical Solution of the Mixed Problem for the Homogeneous Wave Equation with an Integrable Potential

Necessary and Sufficient Conditions for the Existence of a Classical Solution of the Mixed Problem for the Homogeneous Wave Equation with an Integrable Potential

We use the Fourier method to obtain necessary and sufficient conditions for the existence of a classical solution of the mixed problem for a homogeneous wave equation with an integrable potential and fixed endpoints. The solution is represented by a rapidly convergent series.

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Veröffentlicht in:Differential equations 2019-05, Vol.55 (5), p.703-717
1. Verfasser: Khromov, A. P.
Format: Artikel
Sprache:eng
Schlagworte:
Difference and Functional Equations
Differential equations
Economic models
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Wave equations
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Beschreibung
Zusammenfassung:We use the Fourier method to obtain necessary and sufficient conditions for the existence of a classical solution of the mixed problem for a homogeneous wave equation with an integrable potential and fixed endpoints. The solution is represented by a rapidly convergent series.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266119050112